Metamath Proof Explorer
Description: A partially quantified form of mpi similar to bj-almpi .
(Contributed by BJ, 19-Mar-2026)
(Proof modification is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
bj-almpig.maj |
⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) ) |
|
|
bj-almpig.min |
⊢ ∀ 𝑥 𝜒 |
|
Assertion |
bj-almpig |
⊢ ∀ 𝑥 ( 𝜑 → 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
bj-almpig.maj |
⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) ) |
| 2 |
|
bj-almpig.min |
⊢ ∀ 𝑥 𝜒 |
| 3 |
1
|
ax-gen |
⊢ ∀ 𝑥 ( 𝜑 → ( 𝜒 → 𝜓 ) ) |
| 4 |
3 2
|
bj-almpi |
⊢ ∀ 𝑥 ( 𝜑 → 𝜓 ) |